2.3 Debt Valuation Flashcards
What is a yield?
Return on a bond
What are 4 other names for a Flat Yield?
Interest yield
Simple yield
Coupon yield
Running yield
How do we calculate flat yield?
(Gross annual coupon/market price) x 100%
What are the limitations of the flat yield calculation?
- only considering coupon (investor holding bond to maturity cannot get an indication of capital gain/loss)
- uses gross coupon; doesn’t take into consideration impact of tax
In what cases would a flat yield calculation be used?
- purely income-seeking non-taxpayers (not planning to hold bond to maturity)
- irredeemable (undated) bond
What is an irredeemable bond?
aka. undated bond
bond with no known redemption date
What is the relationship between the yield and the coupon?
- if price is same as nominal value; yield and coupon should be the same
- if price of bond > NV: Coupon>FY
- if price of bond < NV: Coupon<FY
What is Gross redemption yield (GRY)?
- considers annual return due to income and gain through to redemption
- annualised total return for bond held to maturity
What is Gross redemption yield (GRY) also known as?
Yield to maturity (YTM)
How doe we calculate of GRY?
Flat yield + Profit/loss at redemption
How do we calculate profit/loss at redemption
(Difference between price and nominal value / number of years till redemption)/ price x 100%
if negative = capital loss
What is relationship between Price, NV, Coupon, FY and GRY
If Price > NV: Coupon > FY > GRY (capital loss)
If Price < NV: Coupon < FY < GRY (capital gain)
What is the Net redemption yield?
Considers impact of tax of GRY (YTM)
How to calculate NRY?
Apply income tax to the coupon - not expected to calculate in the exam
How do we price bonds?
Work out value of future cashflows by discounting future CFs to calculate PV
What is the PV formula?
PV = FV/(1+r)^n
r = discounting factor (interest rate)
n = number of period for which you are discounting
What should we take into account when discounting a bond?
The CF in the final year will always be that year’s coupon + the redemption value
What is the clean price of a bond?
The quoted price
What is the dirty price of a bond?
The clean price + any accrued interest
Difference between cum coupon period and ex coupon period?
Cum coupon period - if someone buys a bond off smn in this period buyer gets next coupon payment
ex coupon period - if smn buys a bond off smn at this period seller gets next coupon payment (eg. a few days before next coupon payment)
Why are bonds with a low coupon attractive?
Coupon received from most bonds is generally taxable, but any gain made on redemption (or subsequent sale) is not taxable
This makes bonds with a low coupon attractive to higher rate taxpayers, as the price may be lower than par, resulting in a part of the return coming in the form of a tax-free capital gain
What is the ex-coupon period for a UK Gilt?
Typically 7 business days
What is the ex-coupon period for a bearer bond?
Do not typically have ex-coupon periods
What is the relationship between clean and dirty prices of bonds in cum/ex coupon periods?
Cum coupon period: Dirty price always higher than clean price
- in this period the buyer gets the whole coupon for the 6 month (or 1 yr period) but a portion of that should go to seller
- seller factors this in and adds on top of clean price
Ex coupon period: Clean price higher than dirty
- because buyer of the bond doesn’t get the few days worth of interest as they don’t get the coupon; seller owes them that portion of interest and does so by discounting price
How do we calculate accrued interest?
𝐴𝑐𝑐𝑟𝑢𝑒𝑑 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 = 𝑃𝑎𝑦𝑚𝑒𝑛𝑡 × (𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑎𝑦𝑠 𝑓𝑟𝑜𝑚 𝑙𝑎𝑠𝑡 𝑝𝑎𝑦𝑚𝑒𝑛𝑡 /
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑎𝑦𝑠 𝑖𝑛 𝑝𝑎𝑦𝑚𝑒𝑛𝑡 𝑝𝑒𝑟𝑖𝑜𝑑)
- work out interest of the nominal and multiply by the fraction (days/days in payment period)
How do we work out clean price?
Divide the nominal by 100 (our assumption) to get the number of bonds
Multiply this by the price at which you are buying
How do we calculate number of actual days?
Start: day after last coupon paid
End: settlement day
What is a spread?
Difference in yield on one investment and yield on another
What are spreads measured in?
basis points (0.01%)
100 basis points = 1%
What is the inter-bank market?
Market where there are reference for interest rates that banks can deposit/borrow from each other
What is LIBOR?
London inter-bank offered rate
- benchmark for inter-bank borrowing
What is LIBID?
London inter-bank bid rate
- benchmark for deposits
What are spread to government securities?
- aka. default spreads
- looks at yield between company and government’s bond (usually for companies in good standing)
What is spread to LIBOR?
Using LIBOR as benchmark
What is spread to swap rates?
- measures spread between 2 yields, one is where the benchmark is the swap rate
- for longer term interest rates
What is simple interest?
Calculation of the simple (annual) interest income on corporate debt
- no compounding
How do we calculate simple interest?
Market price/price per nominal to get number of bonds
interest income (coupon) x number of bonds
What is the conversion ratio for convertible loan stock?
The number of shares that each £100 of nominal value of the bonds can convert into
How do we calculate conversion ratio of convertible loan stock?
nominal value/conversion price of shares
How do we calculate conversion price on convertible loan stock?
Market price/number of shares
how do we calculate conversion premium on convertible loan stock?
Conversion price - current share price
- can express this difference as a percentage of the current share price
How do interest rates affect bond prices?
inverse relationship
- when interest rates rise bond prices fall
- this is because investors demand higher yield when interest rates increase
- if coupon is fixed the only way to achieve this is to lower price
Which bonds are more volatile - longer dated or shorter dated?
The longer the time to redemption the more volatile the bond is - more sensitive to interest rate movements
what is the relationship between price of a bond and time to redemption?
Longer time to redemption = more uncertainty = higher risk = lower price
Which bonds are more volatile?
- long dated
- low coupon (lower income
- low yield
What is modified duration?
- A measure of volatility
- calculates approx. percentage change in bond price for 1% change in interest rates
- bonds w higher modified duration are more volatile
What is a yield curve?
Yield against maturity for a particular benchmark bond
- looks at current yield available to investors across different maturities (time horizons)
What are the different shapes of the yield curve and what do they indicate?
Normal: Upwards sloping
- linked to liquidity preference theory which states that long-dated bonds will have higher yields
Inverted: Downwards sloping
- shorter dated bonds have higher yields
- this suggests expectation of falling rates
- linked to recession
